algoritmosemgrafos

Question Consider the propagation of a virus modeled by the SIS (Susceptible-Infected-Susceptible) system in two distinct networks: A Random Network (Erdős-Rényi). A Scale-Free Network with a degree exponent \(2 Both networks have the same number of nodes \(N\) (where \(N \to \infty\)) and the same average degree \(\langle k \rangle\). Given that the epidemic threshold is defined by the critical spreading rate \(\lambda_c\), below which the virus dies out exponentially, select the correct statement regarding the behavior of this threshold and immunization strategies: A) Since both networks have the same average degree \(\langle k \rangle\), the epidemic threshold \(\lambda_c\) will be identical for both, as the average connection density determines the initial spreading speed in any topology. B) In the Scale-Free Network, the epidemic threshold is given by \(...

Question Consider a network with \( L = 200 \) total edges, composed of multiple communities. Two specific communities, A and B, have total degrees \( k_A = 18 \) and \( k_B = 16 \), with only 2 edges connecting them (\( L_{AB} = 2 \)). Knowing that modularity tends to merge communities when \[ \frac{k_A \cdot k_B}{2L} which of the following statements about detecting these communities is CORRECT? A. Communities A and B will be detected separately because \(\Delta M_{AB} B. The modularity algorithm will inevitably merge A and B due to the resolution limit C. The merger depends exclusively on the number of internal edges in each community D. Such small communities will always have negative modularity E. None of the above Original idea by: Giancarlo Maldonado Cárdenas

A salesperson wants to plan their route between five cities — A, B, C, D, and E — using the Farthest Insertion algorithm. The initial cycle considered is B–D–E–B, highlighted in dark blue in the figure below. The distances between cities (in arbitrary units) are indicated on the edges of the graph: Map of cities and distances Applying the Farthest Insertion algorithm, determine: The order of insertion of cities outside the initial cycle (A and C). The final cycle resulting after all insertions. A) Order: A, C → Final cycle: B–A–D–C–E–B B) Order: C, A → Final cycle: B–D–C–E–A–B C) Order: C, A → Final cycle: B–C–D–E–A–B D) Order: A, C → Final cycle: B–D–E–C–A–B E) None of the above Original idea by: Giancarlo Maldonado Cárdenas